Many applications of mathematical statistics in economics, cryptography, science, technology, etc., employ different kinds of long random number sequences. In some cases, the reliability of statistical analysis is directly related to the "quality of randomness" of the random numbers used.
There are several standard random distributions, such as, Poisson, Bernoulli, etc., each of which can be converted to another. These standard distributions relate to truly random processes, meaning the absence of a statistical correlation between different events or numbers no matter how close or distant from one other they are. Thus, the quality of a random number generator is defined by the proximity of its output to one of these standard truly random distributions.
Generally, random number generators fall into two large categories, algorithmic or physical. An algorithmic random number generator is based on a deterministic mathematical algorithm. The common problem with all algorithmic generators is that according to Kolmogorov's theory of complexity, to generate N truly independent random binary digits, at least 2.sup.N operations must be executed. From a practical point of view, this means that an extremely large number of operations are required even for a moderately sized random number, N. Since existing algorithmic random number generators produce long pseudorandom sequences in a matter of seconds, their complexity is relatively low, and consequently their output sequences are far from truly random. This problem cannot be solved within the framework of an algorithmic approach, and this is why the sequence produced by an algorithmic random number generator is pseudorandom rather than random. In some cases, using a pseudorandom sequence results in misleading analytical conclusions, particularly when large fluctuations of the random inputs make the decisive contribution to the final result.
This does not mean, however, that algorithmic random number generators are useless. The overwhelming advantage of mathematical random number generators compared to almost any kind of natural one is low cost and portability. Many software packages have built-in random number generating capabilities and do not require specialized hardware. The pseudorandom number sequences generated by algorithmic random number generators are suitable for certain applications. Nevertheless, there are applications which require a relatively long string of random numbers without detectable correlations. Furthermore, since an algorithmic "absolute test of randomness" is impossible by definition, the impact of the persistent long-range correlations on the statistical analysis results may become unpredictable, no matter how sophisticated the underlying algorithm is.
By contrast, a natural, or physical random number generator is based on naturally occurring random phenomena, such as thermodynamic or quantum fluctuations, radioactive decay, etc. A radioactive decay is a natural process ideally suited as a source of randomness. Each and every event of a spontaneous radioactive decay does not depend on any external conditions, such as, the quantum state of atomic electrons, presence of other atoms or electromagnetic fields, ambient chemistry, temperature, etc. In this respect, spontaneous radioactive decay is unique. Different kinds of physical random number generators including those based on radioactive decay are known in the art. However, there is room for improvement.
There are two major problems with all existing physical random number generators based on natural radioactive decay. First, the total number of unstable nuclei in a radioactive source gradually decreases in time and so does the mean radiation event frequency. Second, the Poisson time distribution of the events only applies to those ideal sources which display neither secondary radioactive decay, nor any kind of induced radiation which could be later mistaken for a primary radioactive decay. Otherwise, different events, such as the primary and the secondary radioactive decays, become related to one other and thereby correlated in time. These same problems exist in any natural random generator utilizing temporal randomness. The possible physical solution for the above two problems is to utilize a directional randomness of a natural radioactive decay, rather than the temporal randomness. The directional randomness implies that the direction of propagation of emitted radiation produced by individual events is a perfectly random characteristic of the process.
Since it is desirable to provide a random number generator that is designed to eliminate both short and long term correlations in the output, utilizing directional randomness of the physical (natural) process is an appropriate way to solve these problems of the prior art.